Subgroups — #17996391

Order 4736.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924472	C₂	1	2	yes	maximal
2	#14557363	C₂	1	4	yes	maximal, complemented
3	C₂×M₃₂×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596934	—	2	2	no	—
5	#11924472	—	2	2	no	—
6	#11924472	C₂²	1	4	yes	—
7	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
8	M₃₂×C₃₇	C₄	1	4	yes	—
9	C₂×C₁₆×C₃₇	C₂²	1	2	yes	—
10	C₂²×C₄×C₃₇	D₄	1	1	yes	characteristic
11	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
13	C₂×C₈×C₃₇	Q₈	1	2	yes	—
14	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
15	#10596934	—	2	4	no	—
16	#10596934	—	4	2	no	—
17	C₂×#64436	—	4	2	no	—
18	C₁₆×C₃₇	C₂×C₄	1	4	yes	—
19	C₂³×C₃₇	Q₁₆	1	1	yes	characteristic
20	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
21	C₂×C₄×C₃₇	D₈	1	2	yes	—
22	C₂×C₄×C₃₇	Q₁₆	1	1	yes	characteristic
23	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
24	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
25	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
26	C₈×C₃₇	C₂×Q₈	1	1	yes	characteristic
27	#64436	—	4	4	no	—
28	C₂²×C₃₇	—	4	1	no	—
29	C₂²×C₃₇	#107	1	2	yes	—
30	C₂²×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
31	C₄×C₃₇	#107	1	2	yes	—
32	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
33	C₄×C₃₇	C₂×D₈	1	1	yes	characteristic
34	#2161	—	37	1	no	maximal, Sylow
35	C₂×C₃₇	—	2	2	no	—
36	C₂×C₃₇	—	2	1	no	—
37	C₂×C₃₇	C₂×#107	1	1	yes	characteristic
38	C₂×M₃₂	D₃₇	1	1	yes	characteristic
39	C₂×#108	—	37	2	no	—
40	#368	—	37	4	no	—
41	C₃₇	#2161	1	1	yes	characteristic, complemented, Sylow
42	C₂×M₁₆	—	74	2	no	—
43	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
44	M₃₂	Dic₃₇	1	4	yes	—
45	C₂×C₁₆	C₂×D₃₇	1	2	yes	—
46	#108	—	37	4	no	—
47	#108	—	74	2	no	—
48	C₂²×C₄	D₁₄₈	1	1	yes	characteristic
49	M₁₆	—	74	4	no	—
50	M₁₆	—	148	2	no	—
51	C₂×C₈	—	148	2	no	—
52	C₂×C₈	Dic₇₄	1	2	yes	—
53	C₂×C₈	D₁₄₈	1	1	yes	characteristic
54	C₂×C₈	C₂×Dic₃₇	1	2	yes	—
55	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
56	C₁₆	C₂×Dic₃₇	1	4	yes	—
57	C₂³	Dic₁₄₈	1	1	yes	characteristic
58	C₂×C₄	D₂₉₆	1	2	yes	—
59	C₂×C₄	Dic₁₄₈	1	1	yes	characteristic
60	C₂×C₄	C₄⋊Dic₃₇	1	2	yes	—
61	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
62	C₈	—	148	4	no	—
63	C₈	C₄⋊Dic₃₇	1	2	yes	—
64	C₈	C₂×Dic₇₄	1	1	yes	characteristic
65	C₈	C₂²×Dic₃₇	1	1	yes	characteristic
66	C₂²	—	4	1	no	—
67	C₂²	#11924470	1	2	yes	—
68	C₂²	C₂×Dic₁₄₈	1	1	yes	characteristic
69	C₄	#11924470	1	2	yes	—
70	C₄	C₂×C₄⋊Dic₃₇	1	1	yes	characteristic
71	C₄	C₂×D₂₉₆	1	1	yes	characteristic
72	C₂	—	2	1	no	—
73	C₂	—	2	2	no	—
74	C₂	C₂×#11924470	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₂₉₆
commutator	C₈×C₃₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₂×M₃₂×C₃₇	C₂
socle	C₂×C₃₇	C₂×#107
prime radical	C₂³×C₃₇	Q₁₆
cosocle	C₂×C₈×C₃₇	C₂³
hypercenter	C₂×M₃₂	D₃₇
hypocenter	C₃₇	#2161
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #14557363	C₂	semidirect
41. C₃₇	#2161	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#11924472	2
#14557363	2
C₂×M₃₂×C₃₇	2
#2161	37